difference between dimension and scale in blender
Scale is a factor applied to an object non-destructively, on top of its true real
world dimensions. It doesn't really modify in underlying geometry or mesh data unless applied.
A 2 units cube with a scale of 2 will result in a total size of 4 units; a scale factor of 0.5 will result in a final size 1 unit. Scaling doesn't change the actual objects size, so if you enter Edit Mode on a cube with a scale factor of 2 its edges will still show dimensions with a perceived factor of 0.5 in relation to Object Mode because that is their true size.
Also see related Why do the measurements of this object seem erroneous?
Since scale is applied per object, several objects can share the same objectdata (shape defining geometry) but appear to have different sizes because each instance has a different scale factor, despite its geometry being the same and thus having the same true dimensions in Edit Mode.
Object dimensions are the result of the scale factor multiplied by the actual geometry size, and are measured relative to the size of its bounding box. If you change one edge size in Edit Mode it will change the cube's bounding box size, and hence its dimensions.